How to Decide When to Repair

8/12/2019 How to Decide When to Repair

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3. HOW TO DECIDE WHEN TO REPAIR BASICS OF FRACTUREMECHANICS AND FITNESS FOR SERVICE ASSESSMENTS

3.1 GENERAL

The catastrophic and unexpected failure of a bridge member can have severe

consequences. This challenge is well understood by industry and to prevent this

occurrence, non-destructive testing (NDT inspections are employed at regular intervals to

monitor plant condition and reduce the incidence of unplanned outages. The ability of NDT

methods to find flaws before catastrophic failure is dependent upon inspection intervals

and the mechanism of flaw creation. !hile NDT is a step in the assessment of the

condition of plant, it is generally viewed as part of a more comprehensive life assessment

program of critical components. The full component assessment would utilise the

information from NDT as well as metallurgical and stress analyses to determine the

remaining life of a crac"ed or uncrac"ed component before it fails catastrophically.

The tool normally used to assess the significance of a crac" or flaw is #racture $echanics,

which relates the si%e of a flaw to the li"elihood of its causing fast fracture in a given

material under a given stress regime. &enerally spea"ing, the larger the flaw, the lower the

stress at which failure will occur. 'onversely, the lower the service stress the larger the

flaw that may exist without endangering the integrity of the structure.

n circumstances where it is necessary to examine critically the integrity of new or existing

bridges by the use of NDT methods, it is also necessary to establish acceptance levels for

the flaws revealed. The derivation of acceptance levels for flaws is based on the concept

of fitness for purpose. )y this principle, a particular structure is considered to be adequate

for its purpose, provided the conditions to cause catastrophic failure are not reached.

Decisions on whether re*ection and+or repairs are *ustified may be based on fitness for

purpose, either in the light of previously documented experience with similar material,

stress and environmental combinations or on the basis of an engineering critical

assessment ( '/ .

n modern materials science, fracture mechanics is an important tool in improving the

mechanical performance of materials and components. t applies physics of stress and

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strain in particular the theories of elasticity and plasticity, to the microscopic

crystallographic defects found in real materials in order to predict the macroscopic

mechanical failure of bodies. #ractography is widely used with #racture $echanics to

understand the causes of failures and also verify the theoretical failure predictions with

real life failures.

3.2 LINEAR ELASTIC FRACTURE MECHANICS

The critical discontinuity si%e is determined using fracture mechanics principles that relate

stress, flaw si%e, and fracture toughness to existing conditions. f the flaw si%e is less than

the critical si%e, fracture will not li"ely occur and the expected remaining life may be

determined by a fatigue analysis. To ensure this, the stress-intensity factor 7 must be less

than the critical stress-intensity factor 7 ' , 87 ' , or 7 ' , or crac" tip opening displacement

('T9D must be less than the critical 'T9D value : crit . 87 ' is the critical stress-intensity

factor for dynamic loading and plane-strain conditions. 7 ' and 7 ' or 87 ' and 87 ' are

distinguished from each other by material thic"ness and whether conditions are

repsectivelly plane-strain or not. 'ollectively they will be referred to as 7 mat .

;inear lastic #racture $echanics (; #$ first assumes that the material is isotropic and

linear elastic. )ased on the assumption, the stress field near the crac" tip is calculated

using the theory of elasticity. !hen the stresses near the crac" tip exceed the material

fracture toughness, the crac" will grow.

n ; #$, most formulae are derived for either plane stresses or plane strain, associated

with the three basic modes of loadings on a crac"ed body< =$ode = opening, =$ode =

sliding, and =$ode = tearing. These are three basic modes of crac" tip deformation

(#igures >-1 to >-> .



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Figure 3 1! $ode (Tension, 9pening Figure 3 2! $ode ( n-?lane @hear, @liding

Figure 3 3! $ode (9ut-9f-?lane @hear, Tearing .

/gain, ; #$ is valid only when the inelastic deformation is small compared to the si%e of

the crac", what we called small-scale yielding. f large %ones of plastic deformation

develop before the crac" grows, lastic ?lastic #racture $echanics ( ?#$ must be used.

T"e #$%i& LEFM $'$()%i% &$' #e *u+(i'e, $% -*((* %!

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)ased on linear elasticity theories, the stress field near a crac" tip is a function of the

location, the loading conditions, and the geometry of the specimen or ob*ect. n practice,

engineers calculate the stress intensity factor 7 based on the stress field at the crac" tip

and compare it against the "nown fracture toughness of the material-2 and >-> , the stress intensity factor 7 would be

denoted as 7 and 7 respectively.

#or example, for a through crac" in an infinite plate under uniform tension, the stress

intensity factor is as follows as shown in #igure >-3 and quation 1.

Figure 3 /! Through thic"ness crac" on an infinite plate under a tensile load.



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03 1

where a is one half of the width of the through crac".

n the last few decades, many closed-form solutions of the stress intensity factor 7 for

simple configurations were derived.

C($%%i& I'-i'i+e P($+e i+" $ H*(e $', S) e+ri& D*u#(e T"r*ug" Cr$& % U',er

Te'%i*'

03 2

Figure 3 4

C($%%i& Se i i'-i'i+e P($+e i+" $' E,ge T"r*ug" Cr$& U',er Te'%i*'

03 3

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Figure 3 5

C($%%i& I'-i'i+e S+ri6 i+" $ Ce'+re T"r*ug" Cr$& U',er Te'%i*'

03 /

or

03 4

Figure 3 7

C($%%i& I'-i'i+e S+ri6 i+" $' E,ge T"r*ug" Cr$& % u',er Te'%i*'

03 5

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Figure 3 8C($%%i& I'-i'i+e S+ri6 i+" S) e+ri& D*u#(e T"r*ug" Cr$& % u',er Te'%i*'

03 7

Figure 3 9

S6e&i e' Si'g(e E,ge N*+&"e, S6e&i e' U',er Te'%i*'

Figure 3 1:



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03 8

S6e&i e' Si'g(e E,ge N*+&"e, S6e&i e' U',er Be',i'g

Figure 3 11

03 9

S6e&i e' D*u#(e E,ge N*+&"e, S6e&i e' U',er Te'%i*'

Figure 3 12

03 1:

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S6e&i e' Ce'+re Cr$& e, S6e&i e' U',er Te'%i*'

Figure 3 13

03 11

S+re%% I'+e'%i+) F$&+*r $', Fr$&+ure T*ug"'e%%

)ased on the linear theory the stresses at the crac" tip are infinite but in reality there is

always a plastic %one at the crac" tip that limits the stresses to finite values. t is very

difficult to model and calculate the actual stresses in the plastic %one and compare them to

the maximum allowable stresses of the material to determine whether a crac" is going to

grow or not.

/n engineering approach is to perform a series of experiments and reach a critical stress

intensity factor 7 mat for each material, called the fracture toughness or critical stress

intensity factor of the material. 9ne can then determine the crac" stability by comparing 7

and 7 mat directly.

3.2 ELASTIC PLASTIC FRACTURE MECHANICS

;inear lastic #racture $echanics (; #$ applies when the nonlinear deformation of the

material is confined to a small region near the crac" tip. #or brittle materials or materials

that behave in a brittle manner at low temperatures, or if a flaw is severely constrained by

surrounding material resulting in failure by brittle fracture, ; #$ accurately establishes the



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criteria for catastrophic failure. owever, severe limitations arise when large regions of the

material are sub*ect to plastic deformation before a crac" propagates. lastic ?lastic

#racture $echanics ( ?#$ is proposed to analy%e the relatively large plastic %ones.

lastic ?lastic #racture $echanics ( ?#$ assumes isotropic and elastic-plastic materials.)ased on the assumption, the strain energy fields or opening displacement near the crac"

tips are calculated. !hen the energy or opening exceeds the critical value, the crac" will

grow.

?lease note that although the term elastic-plastic is used in this approach, the material is

merely nonlinear-elastic. n others words, the unloading curve of the so called elastic-

plastic material in ?#$ follows the original loading curve, instead of a parallel line to the

linear loading part which is normally the case for true elastic-plastic materials (@ee #igure>-13 .

Figure 3 1/! ; #$ versus ?#$.

Fr$&+ure A'$()%i% U%i'g EPFM

There are two ma*or branches in ?#$< 'rac" Tip 9pening Displacement ('T9D and the

E ntegral. These two parameters are both valid in characteri%ing crac" tip toughness for

elastic-plastic materials.

The basic ?#$ analysis can be summari%ed as follows+2

/ I A.21 P 14 -1>

m I >

(!rought steels have values where / I 3 P14 -1> and m I >

d Determine 87 using the appropriate expression for 7 , the estimated initial

discontinuity si%e a o, and the range of live load stress 8 (i.e., cyclic stressrange . #or cases of variable amplitude loading, an equivalent constant

amplitude stress range, 8 should be computed using equation >-1C. /

live load stress range 8 which is due to cyclic compression stresses, may

be detrimental in regions where tensile residual stress exists. n theseregions, crac"s may propagate, since the addition of tensile residual

stresses will result in an applied stress range of tension and compression.

The stress range, 8 , used to determine fatigue life should be calculatedfrom the algebraic difference of the maximum and minimum stresses even

when the minimum stress is compression and has a negative value, since

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any tensile residual stresses will be superimposed on the applied cyclic

stress (/merican /ssociation of @tate ighway and Transportation 9fficials

166BH /merican nstitute of @teel 'onstruction 1663H $ 1114-2-214A .

( ) m

i

m

ii

E n

n1

=

03 18

!here+2H

T is the temperature at which 7 mat is to be determined (in ' H

T25E is the 25 E 'ON transition temperature (in ' H

) is the thic"ness of the material for which an estimate of 7 mat is required (in mm H

? f is the probability of failure (The use of ? f I 4.4A (A Q is recommended for the purpose

of this annex unless experimental evidence supports the use of other values for a given

material .

quation >-22 is shown for different thic"nesses in #igure >-23 for ? f I 4.4A. The master

curve is not applicable to fully ductile behaviour for which equation >-24 should be used.

Tre$+ e'+ *- %u# %i>e C"$r6) ,$+$

The following applies for 'harpy data measured using sub-si%e specimens for which all

other dimensions except thic"ness are assumed to be as for full-si%e specimens. !hen

plate thic"ness is less than 14 mm, sub-si%e 'harpy specimens are employed. n order to

use the correlations described previously, the shift in transition temperature associated

with the reduced thic"ness of the 'harpy specimen must be allowed for. #or a standard 14

mm square 'harpy specimen, 25 E corresponds to a normali%ed 'harpy energy of >3

E+cm2. The shift in this transition temperature associated with sub-si%e specimen, 8T ss , is

given by the following equation-2> is plotted in #igure >-23.

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Figure 3 2/! Decrease in the 25 E transition temperature which would have been

measured in a full si%e 'ON specimen compared to a sub si%e specimen. ()@ 5614< 1666

/nnex E .

E%+i $+i*' *- T 27J -r* C"$r6) e'ergie% e$%ure, $+ *+"er +e 6er$+ure%

!hen the temperature corresponding to the 25 E 'harpy transition temperature is not

"nown, it can be estimated by extrapolation from 'harpy impact energy values at other

temperatures. owever, because of the range of shapes of 'harpy transition curves, onlyextrapolation over a limited 'harpy energy range is permitted. The recommended values

for extrapolation are given in Table >-1 for given 'harpy values. The downward limit to

extrapolation from T 25E is ->4 ', the upward limit 24 '. These limits should be strictlyadhered to as modern low-', low-@ steels can have steeper transition curves than that

suggested in Table >-1. #or 'harpy energy values exceeding B1 E, a maximum difference

of 24 ' should be assumed.

Di--ere'&e #e+ ee' C"$r6) +e%+ C"$r6) i 6$&+



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+e 6er$+ure $', 27 C"$r6)+r$'%i+i*' +e 6er$+ure

0C

E'erg) 0

->4 A-24 14-14 1C

4 2514 3124 B1

T$#(e 3 1! stimation of T 25E from 'harpy energies measured at other temperatures ()@

5614< 1666 /nnex E . N*+e 1! nterpolation between temperatures is permissible. N*+e 2!

xtrapolations outside the values shown is not permitted. N*+e 3! xample 31 E measured

at T test I -24 ', hence T test - T 25E I 14 ', and T 25E I -(14 - T test I->4 '.

Figure 3 24! 7 mat plotted as a function of the difference between the operating temperature

and the temperature for a 'ON impact energy of 25E. ()@ 5614< 1666 /nnex E .



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Basis of roc!"#r! for $ss!ssi%g Fla&s #si%g '#alit Cat!gori!s

)@ 5614 describes an alternative method of assessing flaws in terms of fatigue life. n this

procedure, flaws are assessed on the basis of a comparison of the @-N curves that

represent the actual and required fatigue strengths of the flawed weld. / grid of @-N curves

is used, each curve representing a particular quality category. The flaw is acceptable if its

actual quality category is the same as or higher than the required quality category. The

approach is similar to that described earlier for the classification of weld category detail

based on expected fatigue live at 2 P 14 B cycles except that the categori%ation is of "nown

flaws in the weld.

The required quality category is determined for the service conditions to be experienced

by the flawed weld. This can be fixed on the basis of the stress ranges and the total

number of cycles of fatigue loading anticipated in the life of the component.

The quality categories refer to particular fatigue design requirements or the actual fatigue

strengths of flaws and are defined in terms of the ten S-N curves shown in #igure >-2B

labelled S1 to S14.

Figure 3 25! Suality category S -N curves ()@ 5614< 1666 /nnex E .

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#urther information on the correct use of this procedure can be obtained from @ection C.A

of )@ 5614< 1666.

Si 6(e E $ 6(e *- $ Re $i'i'g Li-e C$(&u($+i*'

During an inspection of a tension bridge member, a crac" was found at the toe of a butt

weld (#igure >-25 . The butt weld caps were dressed flush with the base metal. The

member was sub*ected to a comprehensive NDT testing survey to accurately determine

the crac" dimensions. /s a result of the survey it was found to be a near perfect elliptical

crac" with the following dimensionsA4 $?a

T$#(e 3 2! 'ollated information.

S+e6 2! f necessary use )@ 5614< 1666 to determine equivalent flaw shapes. n

this case, the crac" is symmetrical, hence there is no need to estimate the equivalent flaw

shape.

S+e6 3! Determine the applicable geometric correction factor to apply from

literature.

n this case we will use the following equations and the diagram shown in #igure >-2C-23 and >-2A-26.

Figure 3 29! 'alculated cycles to failure from 2 mm to A2 mm.

Thus using the above plot and relating cycles to time, suitable inspection and repair

intervals may be established.

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